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Step-by-step Solution

Integral of $\frac{37-11x}{\left(x^2-x-2\right)\left(x-3\right)}$ with respect to x

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Answer

$4\ln\left|x+1\right|-5\ln\left|x-2\right|+\ln\left|x-3\right|+C_0$

Step-by-step explanation

Problem to solve:

$\int\frac{37-11x}{\left(x^2-x-2\right)\left(x-3\right)}dx$
1

Factor the trinomial $\left(x^2-x-2\right)$ finding two numbers that multiply to form $-2$ and added form $-1$

$\begin{matrix}\left(1\right)\left(-2\right)=-2\\ \left(1\right)+\left(-2\right)=-1\end{matrix}$
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Thus

$\int\frac{37-11x}{\left(x+1\right)\left(x-2\right)\left(x-3\right)}dx$

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Answer

$4\ln\left|x+1\right|-5\ln\left|x-2\right|+\ln\left|x-3\right|+C_0$

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